I don't think there should be, actually. I don't think you want to use the prospect of lost money alone to disincentivize third party oversight of a process that would otherwise be a unilateral exercise of league discretion, particularly when the league in question is so bad at it. That would either just disproportionately affect players who don't make as much (if the player bears the cost), or more likely, shift money out of the pockets of the NHLPA and into the pockets of the NHL.
I think what should happen is it should effectively be a hearing de novo - with the result that there's a risk that the arbitrator hands down a bigger suspension than what was originally put in place by the DOPS.
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